A robust geographically weighted LASSO model with Huber Loss for outlier-resilient spatial analysis: application to COVID-19 dynamics in Indian districts

Abstract

Geographically Weighted Regression (GWR) is a widely used technique for modeling spatially varying relationships in epidemiological data. However, its sensitivity to multicollinearity and outliers can limit its reliability in complex datasets, such as those involving COVID-19. To address these limitations, this study first employed the RGWR model, which uses the Huber loss to enhance robustness against outliers. Simultaneously, to handle multicollinearity and enable local variable selection, the Geographically Weighted LASSO (GWL) model is employed. Despite their individual strengths, both RGWR and GWL face challenges when outliers and multicollinearity coexist. To overcome this, we propose a Robust Geographically Weighted LASSO (RGWL) model that integrates the Huber loss function with a spatially adaptive LASSOpenalty. This combined formulation enhances robustness to outliers while effectively performing localized regularization and variable selection. We apply these models to district-level COVID-19 data from India, incorporating a comprehensive set of socio-demographic, environmental, and health-related variables. Comparative analysis reveals that the proposed RGWL model outperforms both RGWR and GWL in terms of predictive accuracy and goodness of fit, particularly in the presence of extreme observations and collinear predictors. The spatially varying coefficients further highlight region-specific patterns, demonstrating the utility of the RGWL model for robust, localized analysis in epidemiological research.